The dependence of the cut-off frequency of the conduction mode electrohydrodynamic instabilities, exhibited by homogeneously aligned negative dielectric anisotropy nematic liquid crystals, on the conductivity of the nematic material, the thickness of the nematic layer and the intensity of an orienting magnetic field, is examined. It is found that for sufficiently high conductivity and/or large layer thickness, the cut-off frequency is proportional to the conductivity of the material, and independent of the intensity of the orienting field. Lowering the conductivity and/or the thickness of the nematic layer results in smaller values of the ratio of the cut-off frequency to conductivity, until a critical limit is reached beyond of which no conduction mode of instability has to be observed. It is found also that for given values of conductivity and thickness, the effect of the orienting magnetic field is to lower the cut-off frequency of the instability and, also, to increase the critical conductivity and thickness values.